One of the most frequent questions I find on Quora is something like “If it is noon at the Greenwich meridian, what time will it be at 61° E
(show your work)?” or “If it is Friday at 9pm on 36 degree East, then what will be the time
at 46 degree West?”. There must be about 4 or 5 a week. Why are there so many such
questions? The answer is completely meaningless, since there's no mention of a latitude,
nor of a time of year. And who could be interested in the answer?

My guess is that this is a frequently posed school homework assignment, as the first
question suggests. This would mean that the teachers are doing their pupils a disservice by
suggesting that there is an answer at all. Still, I hope this page will make it easier to
answer these questions.

If it is noon at the Greenwich meridian, what time will it be at 61° E?

What time is it at the origin?

In this example, all we know is the latitudes at start at end. We need to convert the start
time to UTC. What? Isn't the time at the
Greenwich meridian GMT, the same thing as
UTC?

No. GMT and UTC are not the same, though they're very close, but they can be up to a
second apart. For this discussion, that's not important, so we can assume that GMT is
the same as UTC.

More important, though, when people say “the time at”, they're invariably talking about
local time.

In the UK, that's GMT in the winter,
but BST (UTC+1) in the
summer. And further south, Spain
has CET (UTC+1) in the
winter and CEST
(UTC+2) in the summer. So if the local time is 12:00, the UTC time is 10:00 UTC, 11:00
UTC or 12:00 UTC.

What time is it at the destination?

We need to do something similar at the destination. We only have the latitude, 61° E, so we
need to go north and south and see what time zones it covers.

At 68° N we're in the Russia 2 time zone (UTC+3). Here the time will be 13:00, 14:00 or
15:00.

At 63° N we're in the Russia 3 time zone (UTC+4). Here the time will be 14:00, 15:00 or
16:00.

At 50° N we're in Kazakhstan,
where the time zone is UTC+6. Here the local time will be 16:00, 17:00 or 18:00.

At 40° N we're in Turkmenistan,
where the time zone is UTC+5. Here the local time will be 15:00, 16:00 or 17:00.

At 36° N we're in Iran, where the time
zone is UTC+3:30. Iran observes daylight saving time, so here the time will be 13:30,
14:30, 15:30 or 16:30, depending on the time of year.

At 29.83° N we're in Afghanistan,
where the time zone is UTC+4:30. Here the time will be 14:30, 15:30 or 16:30.

Only a kilometre or two away at 29.81° N we're
in Pakistan, where the time zone is
UTC+5. Here the local time will be 15:00, 16:00 or 17:00.

So there we have it. The answer is “13:00, 13:30, 14:00, 14:30, 15:00, 15:30, 16:00, 16:30,
17:00 or 18:00”.

What did the teacher want?

I'm left with the impression that the teacher (presumably in the large plural) is ignorant
of time zones. He may want to go like this:

Time at Greenwich is 12 pm.

The world has 24 hours spread round 360°. Therefore an hour is 360÷24 or 15°.

To get the time difference, divide the longitude difference by 15. 61÷15 is 4.067 or 4
hours, 4 minutes.

Therefore the time at 61° E is 4:04 pm.

The problem with this answer is that it is wrong. In almost every case above,
the local time at 61° is the same as the time at 60°, where the answer would have been “4
pm”, one of the ten possibilities. If any teachers are reading this, please do your pupils
a service and stop asking such unanswerable questions and expecting answers that are wrong.

If it is noon at GMT, what time is it in Wellington?

This is a slightly more sensible variant of the previous question.

There are several approaches. First, manual:

What time is it at the origin?

Here the origin is ”noon GMT”. GMT is the time zone in the United Kingdom in winter.
It was once used as a base for time zones, but that's
now UTC. We need to convert the start
time to UTC.

What? Isn't the time at the Greenwich
meridian GMT, the same thing as UTC? No.
GMT and UTC are not the same. They're very close, but they can be up to a second
apart. Sadly, many people who mean UTC say GMT.

How do you find the time zone? The Wikipedia link above gives it in the right-hand
information panel: NZST, UTC+12. So the
first approximation would be midnight (24:00 on the same day or 0:00 on the following day).

Our Wellington is in New
Zealand, which uses DST. In the summer the time zone offset is UTC+13, so the time in
the summer would be 1:00 on the following day.

But how do you tell when it's summer? Each country with DST changes at different times,
and Wikipedia's page is no help here. You need a different
one: Daylight
saving time by country, which tells you that DST starts on the last Sunday in
September and ends on the first Sunday in April. With this information, you can decide
whether the time is 0:00 or 1:00 on the following day.

Too much work? You can ask Time Zone Converter, which gives you the opportunity to enter the time. It's
intended for locations, but you can also enter “UTC”. This also allows you to enter more
than two locations. Irritatingly, it displays times in 12 hour format, and I can't find a
way to change it.

Then there's WorldTimeServer, which offers lots of functions, but I haven't found one that helps
here.

If it is Friday at 9pm on 36 degree East, then what will be the time
at 46 degree West?

In this case, the destination longitude mainly transverses ocean. This time I choose
46° W, 65° N, since it's probably
round Greenland. And sure enough,
about the only countries at this longitude are Greenland
and Brazil. As far as I know, neither of
them have Daylight Saving
Time, and they both have a time zone offset of UTC-3:00. So the time there would be
15:00 or 16:00, still on Friday.

What time is it at the origin?

In the example I chose, the time is known at “36 degree East”. Where's that? It's
somewhere in Eastern Europe or Eastern Africa. I start by using Google Maps to find where
36° E, 45° N is. In this case it's
just south of Crimea, which is interesting
in itself. Do you recognize the Russian annexation of Crimea? Then the time zone is EST,
UTC+3:00, all year round. Otherwise the time zone is EET, UTC+2:00 in the winter or
UTC+3:00 in the winter.

But this is just a guess. Let's look at the time
zone map. Further north it could be in Russia. It's just far enough east not to
touch the Norwegian time zone (UTC+1/UTC+2).

And further south? Also nothing of great interest, only UTC+2 or UTC+3. So the time is
either 19:00 or 18:00 UTC.

The time at the destination

In this case, the destination longitude mainly transverses ocean. This time I choose
46° W, 65° N, since it's probably
round Greenland. And sure enough,
about the only countries at this longitude are Greenland
and Brazil. As far as I know, neither of
them have Daylight Saving
Time, and they both have a time zone offset of UTC-3:00. So the time there would be
15:00 or 16:00.

Is this the answer that the teacher wants? Probably not. He probably wants you to take the
difference in longitude, divide by 15 and treat it as a time offset, giving a time of 15:32
(or, as he might prefer it, 3:32 pm). Problem: that's just plain wrong. Everywhere
in the world is in some time zone or another, and the smallest increments (in only a couple
of zones) are 15 minutes.

Local time

Everybody knows what local time is, right? I thought so, anyway. In fact, there's no
accurate definition. For me, it's obvious that it's the time used at a particular location,
in other words as defined by your local time zone.

the standard Time is calculated by time zone only but local time has 4 min difference at
every longitudes. And longitudes play very important roll to calculate the time. there are
24 time zones in the world and according to that question I think this the way to
calculate. and only because of longitudes time can be calculated. Greenwich Prime Meridian
is the base line to divide the world into eastern hemisphere and western hemisphere and
this is the longitude only.

That's not correct, of course. But clearly it's being taught. It seems that some people
(India again?) use the term “local time” to
mean mean solar time, also known
as local mean time, an obsolete
method used to even out the effects of eccentricities in the earth's orbit before the advent
of time zones. There's no basis for this assumption: local time is the time that you will
see on clocks in any specific location, and it's defined by the time zone.

This definition does serve one purpose, though: if I'm correct, it explains these
nonsensical questions, at least when “local time” is specified.

the time based on the meridian through a specific place, as a city, in contrast to that
of the time zone within which the place is located; the time in a specific place as
compared to that of another place to the east or west. Origin of local time. 1825-1835.

local timen. (originally) time at a particular place reckoned from the
instant of transit of the mean sun over the meridian at that place (which defines noon);
(now more usually, and sometimes as a postmodifier) time as reckoned in the time zone
containing the observer or the specified place;

So the meaning changed with the advent of time zones, as one would expect. The quotations
show the last use of the old meaning in 1865:

1865 Catholic World Apr. 127/1 Railway time is gradually beating local time.

And the first clear reference to the new meaning is:

1968 H. Franklin Crash i. 9 Our estimated time of arrival at Cairo is 17.45 local
time, 15.45 G.M.T.